Wikipedia talk:WikiProject Mathematics/Archive/2011/Dec

Opinions at Differentiation rules
What are our opinions of recent edits at Differentiation rules? There is a discussion on the talk page. Sławomir Biały (talk) 02:49, 2 December 2011 (UTC)

Rules of Inference
Hello all. I am not a very active editor, but I saw that Template:Rules_of_inference was missing two important rules (existential generalization and existential instantiation). They are briefly discussed in Existential quantification, but I think that the way the template is organized is very messy. I created a page for existential generalization, but I held off on creating existential instantiation because I did not think it would be prudent to create another stub. Perhaps all four rules of inference can be merged into a new page? Let me know your thoughts on this. Yarou (talk) 06:41, 2 December 2011 (UTC)


 * I agree that the current version is messy&mdash;I like the original version I made much better. In any case, I think making stub articles on existential generalization and existential instantiation is a reasonable idea, since the other rules of inference already have separate articles.  You don't have to add much content yourself, since the idea of a stub is that it should grow over time as other editors contribute. Jim.belk (talk) 03:36, 3 December 2011 (UTC)


 * I've taken the liberty of "tidying up" the template by moving the prepositional statements into pop-ups. See what you think. A further suggestion: the top link in the template to Rules of inference is the ideal place to put a compact list of the rules but it is not yet there; if someone wants the table it would be one click away. Quondum talkcontr 12:48, 3 December 2011 (UTC)

Multivariate resultant
I did not find in Wikipedia any mention of the multivariate resultant (AKA Macaulay's resultant). It is the main tool of elimination theory, but it is not even cited in that page. Someone is willing to write the page? D.Lazard (talk) 17:27, 2 December 2011 (UTC)

Also there is nothing on the subresultants nor on the various (pseudo)remainder sequences which are used to compute the gcd of univariate polynomials over the integers or another polynomial ring. Classical Euclid's algorithm generates fractions which may costly to simplify, and pseudo divisions (another lacking page) generate an exponential growth of the coefficients. D.Lazard (talk) 17:47, 2 December 2011 (UTC)

Complex geometry
As I was examining a number of related stubs; Imaginary point, Imaginary line (mathematics), Real point, Real curve, and Imaginary curve, the thought struck me that these should all be redirects to an article on elementary properties of complex vector spaces and complex projective spaces, which could sort out all these definitions coherently. My initial thought was that this page should be called Complex geometry, as the natural title for someone looking for this type of information. But this page already exists, and while it started out as an elementary version of what I have in mind, it was "hijacked" with the argument that Complex geometry technically means the study of complex manifolds and functions of several complex variables in the mathematical research community. The material that was on the page was dumped into Complex analytic geometry; perhaps a more accurate title for the content, but much harder to find if you're not familiar with geometric taxonomy. This was all done 4-5 years ago and the Complex geometry page, consisting now of the above technical definition and one additional sentence, has remained a stub. I propose re-aligning the page to talk about elementary definitions and properties of some complex manifolds and directing readers wanting a more advanced treatment to the well developed Complex manifold page. Comments? Bill Cherowitzo (talk) 05:31, 3 December 2011 (UTC)


 * This seems to be a common issue on Wikipedia. Ring theory is nothing more or less than the study of rings. So does it even deserve its own Ring theory article, separate from Ring (mathematics)? Complex geometry is the study of complex manifolds. So does it deserve its own article? I honestly don't know. In any event, I think that Complex geometry should discuss whatever mathematicians call complex geometry. Your examples could be mentioned prominently in the intro section. Mgnbar (talk) 06:09, 3 December 2011 (UTC)


 * Complex geometry seems not really used in modern mathematics. Algebraic geometry and Analytic geometry are usually preferred; this why is I have added the first paragraph in analytic geometry. Indeed, all the links in complex geometry refer to analytic geometry (modern meaning). Thus propose to rewrite complex geometry as proposed by Bill Cherowitzo, simply mentioning at the beginning that complex geometry is also another name for analytic geometry (modern meaning). D.Lazard (talk) 09:21, 3 December 2011 (UTC)


 * The articles listed above are an example of a walled garden. In general there is a tendency on Wikipedia to create a number of stubby articles where a single article of acceptable quality should be created. This project may be especially susceptible due to the influence of MathWorld which is full of such things (see Trovatore's comments a few threads back). We should cover material on elementary analytic geometry but with complex coefficients, for example the fact that if a line intersects the real plane more than once then it does so in a real line. This has nothing to do with complex manifolds and our material on algebraic geometry tends to skip over this kind of thing and go on to topoi and Grothendieck cohomology. (See however Focus (geometry).) Imo the material should be merged but probably into several different articles. Specifically Imaginary point and Real point into Complex projective plane; Imaginary line (mathematics) into line (geometry); and Complex analytic geometry, Real curve, and Imaginary curve into a new section of Analytic geometry.--RDBury (talk) 10:57, 3 December 2011 (UTC)

The discipline of "complex geometry" certainly does exist. There are people out there studying complex manifolds and complex (analytic) spaces using a mixture of analytic, algebraic and geometric techniques; my research supervisor is one of them. Older work in this area was usually classified under the name "several complex variables", but during the last couple of decades more people have started to use the word "geometry". The title "complex analytic geometry" is more restrictive, and doesn't cover the full range of this subject. "Analytic geometry" intersects complex geometry but isn't the same thing; there are also real analytic geometers out there who aren't interested in complex spaces. Wikipedia's coverage of this whole area is rather sketchy; it's not good to try and draw conclusions about the nature of a discpline solely by what's represented on this web site. Jowa fan (talk) 13:02, 3 December 2011 (UTC)


 * I'm not sure that I'm convinced of any of the proposed merge/redirect targets. For instance, I would associate "real point" and "real curve" with real algebraic geometry.  At least, these terms are seldom used in the context of complex projective space by itself.   Sławomir Biały  (talk) 13:14, 3 December 2011 (UTC)


 * For what it's worth, my personal experience agrees with Jowa fan's, that "complex geometry" is a term in current use by mathematicians. For what it's worth, the Mathematics Subject Classification has "Real and complex geometry" (51Mxx) and "Complex manifolds" (32Qxx). Mgnbar (talk) 17:25, 3 December 2011 (UTC)

Let's not get too far away from the intent of my post. I am really interested in the most appropriate way to deal with this "walled garden" (thanks for that term!). I am not claiming that "complex geometry" isn't used in the research community, it clearly is (a google search indicates this ... although an argument can be made that the most popular use of the term is for a line of leather clothing). What I am proposing is an abuse of that title – which is why I've brought up the issue here. I agree with RDBury, our coverage of elementary algebraic geometry is a bit weak and too scattered, making it hard for readers to get an introduction to the advanced topics; so I see a need to fill this gap. My thinking is that by using a very classical interpretation of "Complex geometry" we can take a page which serves no real function and turn it into something that could be fairly useful. Anyone coming to this page looking for the modern meaning would be directed to the appropriate place, while those who are naively searching will actually get to something that they may be looking for. Bill Cherowitzo (talk) 18:43, 3 December 2011 (UTC)


 * Sorry to have been the cause of a discussion away from the intent of Wcherowi post. I fully agree with his proposition. D.Lazard (talk) 19:05, 3 December 2011 (UTC)


 * Would a disambiguation page not be best? Quondum talkcontr 20:53, 3 December 2011 (UTC)

Niven's theorem
Niven's theorem states that the only rational multiples of $\pi$ whose sine is rational are the ones you learned in childhood: sin 0&deg;, ±sin 30&deg;, and ±sin 90&deg;. The article is new. Work on it if you are so moved. (Currently it does not include a proof and there are just two references. Also, there may be more articles that ought to link to it than currently do.) Michael Hardy (talk) 18:48, 3 December 2011 (UTC)
 * Are you sure the theorem is due to Niven? Hermite proved that exp(r) is irrational when r is rational; I was sure that irrationality of sin(r) was proved around the same time. Sasha (talk) 21:34, 3 December 2011 (UTC) Quotation from Niven (which is consistent with my claim):

The central result, Theorem 3.9, was proved by D. H. Lehmer, Amer. Math. Monthly, 40 (1933), 165-166. The extension to the tangent function in Theorem 3.11 has not been given elsewhere, so far as we know. A proof of Corollary 3.12 independent of Theorems 3.9 and 3.11 was given by J. M. H. Olmsted, Amer. Math. Monthly, 52 (1945), 507-508. The topic is a recurring one in the popular literature: as examples we cite B. H. Arnold and Howard Eves, Amer. Math. Monthly, 56 (1949), 20-21; R. W. Hamming, Amer. Math. Monthly, 52 (1945), 336-337; E. Swift, Amer. Math. Monthly, 29 (1922), 404-405; R. S. Underwood, Amer. Math. Monthly, 28 (1921), 374-376.
 * Here "Cor. 3.12" is what Michael called Niven's theorem, it follows from Thm. 3.9. Here is a link to Olmsted for your convenience. Sasha (talk) 22:38, 3 December 2011 (UTC)
 * PS The only place I have found where the result is called Niven's thm. is mathworld, which is not necessarily reliable (see discussion above).
 * I agree about Mathworld, especially regarding neologisms, but something like it (but with tan instead of sin) is called Niven's thm here. —David Eppstein (talk) 01:31, 4 December 2011 (UTC)
 * google does not show me this page in your ref, what is the statement there? In any case, my main argument is that Niven himself cites an earlier reference for this result. Sasha (talk) 05:32, 4 December 2011 (UTC)
 * The relevant part of that page says "...we see that $$\tan(\pi/t)$$ is rational; it follows by Niven's theorem that $$t=4$$." —David Eppstein (talk) 06:06, 4 December 2011 (UTC)
 * I think we should add a ref a) to Lehmer (whose theorem implies the result immediately) and to Olmsted. Both preceded Niven. Sasha (talk) 16:28, 4 December 2011 (UTC)
 * I am copying this discussion to the talk page. Sasha (talk) 00:29, 6 December 2011 (UTC)

Torsten Carleman
A new editor removed "Jewish chatter" about Carleman's alcoholism, etc.

Given my recent blocking (involving the phrase "national socialism"), I would appreciate if another would deal with this editor, who is active also on Swedish Wikpedia.

Thanks, Kiefer .Wolfowitz 12:52, 4 December 2011 (UTC)

Upright "d" versus italic "d"
Some relatively new editors seem to be on a campaign to change all of our italic d's in differentials into upright d's. (See Special:Contributions/193.2.120.35, and recent edits to Differential of a function.)  I think we need to get some firm consensus on how to deal with this trend. This seems to be a convention that is substantially in the minority in the mathematical sciences, although maybe some subfields prefer the upright "d" (whence the small but dedicated group that wants to change everything to their way). I have examined many of the textbooks on my shelves. These include texts in mathematics, physics, computer science, aimed at all levels of higher education (from a number of textbooks for first year calculus to research monographs), and I have yet to find a single example of an upright "d" used for the differential. There is allegedly an ISO standard (ISO 80000) that recommends the upright "d". Can anyone confirm this? At any rate, I don't see that our typography is necessarily dictated by the ISO. Sławomir Biały (talk) 13:46, 5 December 2011 (UTC)
 * I don't have a problem with having some standard to go by, but my problem with ISO is it isn't free. NIST is free but as I recall there were objections to it because it describes USA usage rather than international. My recollection of the outcome of the discussions of the several similar issues like this that have come up in the last few months is that establishing standards can be bad since different notations are in common use depending on the area of mathematics, for example mathematical physics might use a different notation than is used in probability. The upshot seems to be a "leave well enough alone" policy, i.e. don't change the notation just because it's not quite what you're used to or because it differs from another article. I suppose this has precedent in WP:MOS though from what I've seen this doesn't really eliminate the pointless spelling edits that happen because some people prefer a 'u' in 'color'. So I think reverting these edits was appropriate since it goes against the usage already established in the article, but going by previous discussions I don't think we can go as far as establishing a standard.--RDBury (talk) 14:31, 5 December 2011 (UTC)
 * I give the "standards" very little weight, since I have never, ever, seen a book or advice on writing mathematics that refers to any of them. I would say we should make a survey of a couple dozen analysis and calculus books and see if there is any pattern in the use of upright or italic. &mdash; Carl (CBM · talk) 14:42, 5 December 2011 (UTC)
 * Actually, the issue is already covered in MOSMATH, see the last paragraph of WP:MOSMATH which basically reiterates the "leave well enough alone" policy.--RDBury (talk) 14:43, 5 December 2011 (UTC)
 * I agree in general, but at the same time actual evidence about how often upright ones are used might be interesting and useful for the discussion. &mdash; Carl (CBM · talk) 14:48, 5 December 2011 (UTC)
 * (e/c) I realize that, but lately I'm finding that I have to tell off a lot of people who think that the upright "d" is "clearly" better, that anything else is "sloppy" or "lazy". It's better to have a substantive retort to such individuals, rather than just stating that it's a matter of personal editorial style.  I've been pointing out that Donald Knuth and Mike Spivak prefer the italic d, and that none of the hundreds of books on my shelf seem to use an upright "d".   Sławomir Biały  (talk) 14:51, 5 December 2011 (UTC)
 * See Maxwell's equations, this has used upright 'd' for several years now so it's not the result of recent revisionism.--RDBury (talk) 14:57, 5 December 2011 (UTC)
 * No doubt there will be some that use an upright d. Rather than arguing for standardizing, I am just saying that the best argument for why not to unilaterally adopt some unknown ISO standard is that few math books don't do so. &mdash; Carl (CBM · talk) 14:59, 5 December 2011 (UTC)

The argument for the upright "d" seems to be that it leaves the letter d available for use as a variable, like all variables in its italic form. Thus one can unambiguously write
 * $$ \frac{\mathrm{d}d}{\mathrm{d}x} \, $$

But that's a pretty minor advantage, and I hardly ever see the upright "d" used this way in print. I think maybe in the writings of physicists it may be more frequently seen, but I'm not sure. Michael Hardy (talk) 15:16, 5 December 2011 (UTC)
 * I don't think a survey can really settle an issue like this. The bookshelves of the people in this project are certainly skewed toward pure mathematics and the bookshelf for someone in theoretical physics might give very different results. Really you'd have to survey an entire library to avoid selection bias and that's just not practical, especially since this kind of issue keeps popping up. How about limiting the survey to those sources that are used as references for the article in question? This would be consistent with subfield specific variations and might have the pleasant side effect of encouraging people to add references to articles.--RDBury (talk) 15:42, 5 December 2011 (UTC)
 * That seems like a good way to handle individual articles. I think the only thing a survey like this could establish is that usage is indeed varied in practice, so that there's no one-size-fits-all solution. That may seem obvious but having actual data somehow makes it more compelling. At least it only has to be done once. I expect that there will be many books of both sorts, and then we can link to the list from a footnote in the MOSMATH to point that out. &mdash; Carl (CBM · talk) 15:55, 5 December 2011 (UTC)


 * This seems like a fairly reasonable proposition to me, the only question remains is how to handle the cases when the references are fairly split. Thenub314 (talk) 16:54, 5 December 2011 (UTC)
 * In cases like that, we often defer to the first major contributor, just as a way to break the tie. &mdash; Carl (CBM · talk) 17:50, 5 December 2011 (UTC)
 * Just in reviewing MOS:MATH, it says "On the other hand, for the differential, imaginary unit, and Euler's number, Wikipedia articles usually use an italic font, so one writes...". I think that the arguments already given, plus this definite recommendation for the italic d (not even counting the survey below) gives pretty firm grounds to revert anyone making sweeping changes to upright (notwithstanding my own unstated preference ;)). Quondum talkcontr 18:36, 6 December 2011 (UTC)

Survey on notation for differentials
Which authors use upright or italic "d" in differentials?

Italic

 * 1) Abbot, Understanding Analysis (Springer, Undergraduate Texts in Mathematics)
 * 2) Abramson, Information theory and coding
 * 3) Ahlfors, Complex analysis
 * 4) Anton, Calculus
 * 5) Aris, Vectors, tensors, and the basic equations of fluid mechanics
 * 6) Bartle, Elements of Real Analysis
 * 7) Beckman, Probability in communication engineering
 * 8) Billingsley, Probability and measure
 * 9) Boas, Mathematical Methods in the Physical Sciences
 * 10) Bourbaki, Elements of the History of Mathematics
 * 11) Bourbaki, Integration
 * 12) Cauchy, Leçons sur le Calcul différentiel
 * 13) Doran/Lazenby, Geometric Algebra for Physicists
 * 14) Eveleigh, Introduction to control systems design
 * 15) Eyges, The classical electromagnetic field
 * 16) Franks, Signal Theory
 * 17) Feynman, Leighton, Sands, The Feynman lectures on physics
 * 18) Folland, Real Analysis
 * 19) Glasserman, Monte Carlo Methods in Financial Engineering
 * 20) Gold/Rader, Digital processing of signals
 * 21) Goldstein, Classical mechanics
 * 22) ter Haar, Elements of statistical mechanics
 * 23) Halmos, Measure Theory
 * 24) Harris F.J., Multirate signal processing for communication systems
 * 25) Helstrom, Statistical theory of detection
 * 26) Hoel/Port/Stone, Introduction to stochastic processes
 * 27) Hughes-Hallett, Gleason, Calculus
 * 28) Jackson, Classical electrodynamics
 * 29) Katznelson, An Introduction to Harmonic Analysis
 * 30) Kreyszig, Advanced engineering mathematics
 * 31) Knuth, Art of computer programming
 * 32) Landau and Lifschitz, A course of theoretical physics
 * 33) Larson and Edwards, Calculus
 * 34) Mehrotra, GSM system engineering
 * 35) Moon/Stirling, Mathematical methods and algorithms
 * 36) Pathria, Statistical mechanics
 * 37) Peskin and Schroeder, An introduction to quantum field theory
 * 38) Rabiner/Gold, Theory and application of digital signal processing
 * 39) Rabiner/Juang, Fundamentals of speech recognition
 * 40) Rabiner/Schafer, Digital processing of speech signals
 * 41) Ralston, A first course in numerical analysis
 * 42) Rendall, Partial Differential Equations in General Relativity
 * 43) Riley, Hobson, Mathematical methods for physics and engineering
 * 44) Ross, Elementary Analysis (Springer UTM)
 * 45) Rudin, Principles of Mathematical Analysis
 * 46) Rudin, Real and Complex Analysis
 * 47) Shirley, Fundamentals of computer graphics
 * 48) Shreve, Stochastic calculus for finance
 * 49) Spivak, A comprehensive introduction to differential geometry
 * 50) Stewart, Calculus 6th ed. (popular textbook in the US)
 * 51) Thomas' calculus
 * 52) Quantum Fields and Strings: A Course for Mathematicians
 * 53) Vaidyanathan, Multirate systems and filter banks
 * 54) Van Trees, Detection, Estimation, and Modulation Theory
 * 55) Viterbi, Principles of Coherent Comunication
 * 56) Wackerly/Mendenhall/Scheaffer, Mathematical statistics with applications
 * 57) Weinberg, Gravitation and cosmology
 * 58) Wilczek, Fractional Statistics and Anyon Superconductivity
 * 59) Wozencraft/Jacobs, Principles of communication engineering

Upright

 * Bostock & Chandler, Mathematics - the core course for A-level (Nelson Thornes, 1981) (introduced on page 112)
 * Capinski and Kopp, Measure, Integral, and Probability (Springer Undergraduate Mathematics Series)
 * Alan Jeffrey, Mathematics for Engineers and Scientists
 * Penrose, The Road to Reality (Vintage)
 * Uses upright d for both standard and exterior derivative


 * Charles Nash and Siddhartha Sen, Topology and Geometry for Physicists
 * Well in fact they seem to use upright d for the exterior derivative and italic d for the covariant exterior derivative. The upright one appears in integrals, derivatives, and differential forms. Plus it gets it wrong occasionally I think but I'm not surprised! Dmcq (talk) 15:24, 5 December 2011 (UTC)


 * Abraham Robinson, Non-standard Analysis
 * The Princeton Companion to Mathematics

Yuri Linnik
The image of Yuri Linnik was nominated for deletion. Could an expert in copyright please check whether the image File:Yuri Linnik (photo).jpg is OK (and if yes, how to tag it properly)? Thanks, Sasha (talk) 05:25, 6 December 2011 (UTC)
 * I'm not exactly an expert in this area, but I added a fair use rationale. Others who know better how to do this are welcome to fix it up better. —David Eppstein (talk) 06:33, 6 December 2011 (UTC)


 * The photograph was produced by the Soviet Union which did not recognize copyright. So I think it would be in the public domain. I have seen such claims on other photographs. But I am not an expert. JRSpriggs (talk) 06:38, 6 December 2011 (UTC)
 * I think we'd have to provide evidence that it was published early enough, if we wanted to cover it that way. I mean, it was certainly shot prior to 1973, but are we sure of its publication date? —David Eppstein (talk) 06:46, 6 December 2011 (UTC)


 * I think it's impossible to win arguments of this particular type except by exhaustion or misdirection, because Wikipedia official policy is impossibly strict. I ran into the problem in connection with Louis Victor Baillot (1793–1898), the last survivor of the Battle of Waterloo. There is an extant photograph of him, which I wanted to upload. But it is conceivable that the photograph is still under copyright protection, and I cannot prove otherwise. The policy is practical only because in most cases it is ignored. Here is a very typical example: File:Maria_Goeppert-Mayer.gif is a photograph of Nobel laureate Maria Goeppert-Mayer, taken in her youth. The description page claims that the photograph is public domain because its copyright term has expired, being life of the author plus 70 years.  In order for the copyright term to have expired, the author would have had to have died before 1941.  The picture was apparently taken around 1930, and the description page also has no author information.  So the copyright may have expired, but it probably hasn't.  This issue has been raised on the image talk page (where it was ignored) and I raised it on Wikipedia talk:Copyrights and it was waved off. I want to end with some helpful advice, but the only thing I can think of that is not depressingly cynical is that David Eppstein's fair use claim is probably the best way to go. Sorry. —Mark Dominus (talk) 14:47, 6 December 2011 (UTC)


 * thank you very much for the help! Sasha (talk) 16:22, 6 December 2011 (UTC)

Geometric formulas
The article titled Geometric formulas is at best quite weak. Is it worth developing? Michael Hardy (talk) 17:41, 5 December 2011 (UTC)
 * It is not only weak, it is an orphan. I have just tagged is as orphan. D.Lazard (talk) 18:27, 5 December 2011 (UTC)
 * I don't think that it's worth developing. It's not clear what the scope of the list is. What should and should not eventually be included? The Riemann-Roch theorem? The word "formula" in the title suggests to me that it was not written by a mathematician. But if one non-mathematician found it valuable to create this list, then maybe others would find such a list useful too. Mgnbar (talk) 19:52, 5 December 2011 (UTC)
 * I think there is scope for a reference article for non-mathematicians. Something like Table of formulae in elementary geometry, that could include things like the volume of a cone, area of a trapezoid, etc.  There are standard tables like this in print encyclopedias too.  (It's also possible that such an article already exists, and this one should be redirected there.)   Sławomir Biały  (talk) 19:59, 5 December 2011 (UTC)
 * A Table of formulae in elementary geometry could be useful if fairly complete. For example the numerous formulas for the triangle may be found in Triangle article, but they are mixed with explanations. For someone which needs to retrieve a forgiven formula, consulting a list of formulas is better than extracting it from the middle of the explanations in a detailed article. For coherency of Wikipedia, such an article would better named List of formulas in elementary geometry. We could rename Geometric formulas in this way and tag it as a stub (to be expanded). D.Lazard (talk) 20:49, 5 December 2011 (UTC)

Discussion copied into Talk:Geometric formulas. D.Lazard (talk) 11:06, 8 December 2011 (UTC)

Merge proposal (Special angle relationships)
There is a proposal to merge several articles relating to angles in elementary geometry into a single article. See Talk:Vertical angles if interested.--RDBury (talk) 14:09, 7 December 2011 (UTC)

Move Encyclopaedia of Mathematics?
The name of Encyclopaedia of Mathematics is now 'Encyclopedia of Mathematics' (the 'a' was dropped); any objections to moving the article to the new name over the existing redirect?--RDBury (talk) 16:03, 8 December 2011 (UTC)
 * I have no opinion on the name. It would be good to have some good independent sources though.  This article is a bit big to be called a stub.  Yaris678 (talk) 16:40, 8 December 2011 (UTC)


 * oh, that's why it became less encyclopaedic no objections from my side. Sasha (talk) 16:42, 8 December 2011 (UTC)
 * Less encyclopaedic, but more encyclopedic. --Trovatore (talk) 01:47, 9 December 2011 (UTC)


 * I moved it. CRGreathouse (t | c) 01:18, 9 December 2011 (UTC)

Also it might be interesting to note, that Springer has switched its encyclopedia to a Mediawiki and a community editing (with editorial supervision by board though). Another consequence of this software switch is, that is looks like that all old links to its articles are dead. Is there a chance to use bot to fix them. If we have a template for the encyclopedia that would need fixing too.--Kmhkmh (talk) 23:08, 10 December 2011 (UTC)
 * See the discussion above .--Salix (talk): 00:00, 11 December 2011 (UTC)
 * Ah thanks I had overlooked the one above.--Kmhkmh (talk) 01:41, 11 December 2011 (UTC)

Water retention on mathematical surfaces
Water retention on mathematical surfaces has been nominated for deletion. Maybe it's just a matter of adding more sources from the literature. Opine at Articles for deletion/Water retention on mathematical surfaces. Michael Hardy (talk) 04:17, 13 December 2011 (UTC)

Frac, FracText, etc.
I think the discussion should best be done here, as to the proper use of frac, fracText, frac/sandbox, etc. It certaily needs to be done somewhere in a single location. The present users of frac might object to replacement with the stacked version, even if it could be done cleanly with the sandbox modifications working. Perhaps the talk pages of WP:MOSMATH or WP:MOSNUM would be a better place for the discussions. — Arthur Rubin (talk) 16:58, 10 December 2011 (UTC)
 * For your consideration: the sandbox version of frac now diplays stacked fraction porerly. See Template:Frac/testcases. — Edokter  ( talk ) — 13:08, 13 December 2011 (UTC)

Non-implemented integral signs
Can everyone please see this link when they have time? It is a proposed workaround for including the closed double and triple integral symbols not possible with LaTeX. They are rendered JPEG images:

\oiint and \oiiint:
 * OiintLaTeX.jpeg OiintLaTeX.jpeg ,
 * OiiintLaTeX.jpeg OiiintLaTeX.jpeg.

and as templates:, , and. I had high hopes for templates, unfortuatley they didn't work out as well the the pure images. ''Thanks - feel free to criticize as heavy as you will, all comments very welcome... ''--F&#61;q(E+v^B) (talk) 00:05, 13 December 2011 (UTC)


 * First point of citisism... JPEGs are blegh. Convert them to PNGs and size them as TeX would output them. The reason the templates don't work is because the images are wrapped in tables, which cannot be displayed inline. Simply remove the table. — Edokter  ( talk ) — 14:40, 13 December 2011 (UTC)


 * Right, as I have pointed out as well before for the table issue. And when uploading PNG versions, please use a transparent color for the background. Thanks. Nageh (talk) 15:09, 13 December 2011 (UTC)
 * Yes, in the default skin I use the background is not white but a very light bluish gray on top of which I can see the background white rectangles for these images very distinctly. Also, you should antialias them, right now they have a bad case of the jaggies. —David Eppstein (talk) 17:00, 13 December 2011 (UTC)

I didn't realize so many people would answer so quickly. The next step then is to upload a new version of the files as PNG and on a transparent background. However - why the statement "size them as TeX would output them"? They already are the correct size. Even if they arn't anyone can still change the size by going to the template page and editing the image syntax. Thats the least of the problems.

As updated on the talk page here, templates are no longer a problem - cheers to Nageh. Thanks for feedback though.--F&#61;q(E+v^B) (talk) 18:17, 13 December 2011 (UTC)

Additional opintions needed at Partition (number theory)
There is an on-going dispute, with fourth revert cycles now, on whether material from a paper on arxiv.org should be included in the article. Some impartial assistance is needed to resolve the issue or find a compromise.--RDBury (talk) 12:22, 14 December 2011 (UTC)

History of the first magic square
I was surprised to find that the Lo Shu Square article had essentially no information on its origin. For example, it does not give the first source in which it is known to have appeared -- or, for that matter, any source in which it appeared.

It does mention an apocryphal origin tying it to Yu the Great. I've seen other origin legends going ll the way back to (if I understand them properly) Fu Xi.

Any historians of math (or historians, or interested amateurs, or people who read Chinese) who can help?

CRGreathouse (t | c) 02:17, 15 December 2011 (UTC)


 * Finding all the transliterations might help a bit, I've seenit also under 'luo shu'. I stumbled across this book (I think) in the library a while back: I'm not very sure how informative it is but it might be a place to start. Rschwieb (talk) 01:52, 16 December 2011 (UTC)


 * The title worries me... I'm pretty well convinced that there are no extant sources older than 2500 years (and probably none older than 1950 years). But I'll look the book up, thanks for the heads-up.
 * CRGreathouse (t | c) 06:54, 16 December 2011 (UTC)


 * I also looked in which I thought might have something, but not that I could see. CRGreathouse (t | c) 07:25, 16 December 2011 (UTC)

author field at template:mactutor
Hello colleagues,

User:Daniele.tampieri suggested to add an "author" field to the template. Please comment at Template_talk:MacTutor.

Sasha (talk) 16:12, 15 December 2011 (UTC)

Encyclopaedia of Mathematics
According to Encyclopaedia of Mathematics and a quick look at the website the EoM is now an open wiki at a new site. This raises a couple of concerns: (related to the above thread they use MathJax as well as MediaWiki - see their front page for info).-- JohnBlackburne wordsdeeds 21:16, 29 November 2011 (UTC)
 * The template SpringerEOM has been updated to the new URL but it looks like all of the pages have new paths to them, so all links are broken.
 * As an open wiki there's no guarantee of the quality of it. I suspect it will be largely unchanged, but it could be updated significantly, in particular with content from WP as it has a similar licence. If it becomes too much like a WP mirror then its value as a reference or for external links will be severely diminished.
 * As a general rule, an encyclopedia should not use another encyclopedia as a reference, no matter how good it is. If I recall correctly, we allow citing tertiary sources on a "better than nothing" basis, but whenever possible the citation should be changed to reflect the secondary source actually used (or some other reliable secondary source).  External links are a fuzzier question. --Trovatore (talk) 21:26, 29 November 2011 (UTC)
 * According to the site they have an editorial board to monitor changes, which is more or less what OEIS does. Unlike WP, you are required to create an account before you can make any edits. You are encouraged to provide your real name when you create the account but (unlike OEIS) it's not mandatory. Also, just looking at the source for a random article, the math formulas were not converted to TeX when they imported the old version, so if you want to make a change you need to create the formula from scratch. It would be a good idea to keep an eye out for errors or other issues being introduced into site, but Springer has quite a reputation to uphold so I doubt they will allow problematic material to exist for long. I agree with Trovatore that ideally secondary sources should be preferred over tertiary, I wouldn't hesitate to use EoM as a reference though if a textbook reference can't be found without a trip to the library. We have such a backlog of unreferenced material that the secondary/tertiary issue isn't that important for the cites we do have.--RDBury (talk) 13:59, 30 November 2011 (UTC)
 * This seems to be about the right balance. Also, although the quality of the EoM is generally uneven, I have found many of the entries to be quite good references even in the presence of secondary sources for the same material.  I don't think it's a good idea to replace links to the EoM with secondary sources, like Trovatore suggests.   Rather, we should try to give additional secondary sources.   Sławomir Biały  (talk) 14:09, 30 November 2011 (UTC)
 * I am the product manager at Springer responsible for managing the technical implementation of the new EOM wiki. I have adapted the citation template documentation for the template:SpringerEOM to use the proper naming convention for the new site. I will be closely watching the site's incoming traffic from WP and updating the ids of WP citations that used the template so that their link-outs will resolve to not only the correct article in the new EOM wiki, but to the version of the article that is identical to the version previously hosted at eom.springer.de.--Nbrothers (talk) 16:13, 30 November 2011 (UTC)
 * I don't know enough about the EoM wiki to make judgments about its level of editorial control and reliability. In the past I've been fairly pleased with the quality of their articles: they are short but informative. I hope they will keep their quality level high. CRGreathouse (t | c) 16:29, 30 November 2011 (UTC)
 * One thing that might require some discussion is whether to link to the original version of the article as Nbrothers is doing, or link to the the current version of the article. Linking to the original is done by using the oldid parameter in the id field of the template. I'm thinking that, especially for links in External links sections, linking to the current version would be more appropriate. Btw, the new article URLs follow WikiMedia's naming conventions, so figuring out what they are from the article names should be straightforward.--RDBury (talk) 17:45, 30 November 2011 (UTC)
 * If the most recent version on an article can be cited, that makes citations much simpler, i.e., following wiki naming convention and no oldid. --Nbrothers (talk) 22:50, 16 December 2011 (UTC)
 * Another idea is to add the new site to Interwiki map so interwiki links can be used rather than URL's, though I'm not sure if this would be compatible with the way the current template works. I don't see any possible downside since people can always use the template if they want, and having an option that saves having to paste in URLs could be useful.--RDBury (talk) 18:17, 30 November 2011 (UTC)


 * Guys, I really do think we should try harder to hold the line against citing encyclopedias. Here's the most important reason, honestly: MathWorld.  MathWorld is an absolute menace to the mathematics articles; if people start adding stuff from there, our quality is seriously threatened.  But it is hard to explain to enthusiastic amateurs just exactly what's so bad about it.  If we can just say, "look, we don't do encyclopedias", that's easier. --Trovatore (talk) 21:23, 30 November 2011 (UTC)
 * I don't see the problem with MathWorld (some of their articles are still better than ours), but I agree that tertiary sources should be avoided whenever practical. CRGreathouse (t | c) 21:29, 30 November 2011 (UTC)
 * See Articles for deletion/Radical integer and Articles for deletion/Regular number. --Trovatore (talk) 01:14, 1 December 2011 (UTC)
 * I agree that Mathworld is pretty bad. Springer EoM is much better and more reliable.  The difference is that the EoM is published by Springer (a very respected scientific publisher) and written by experts, whereas Mathworld is published by Wolfram, and written by a dilettante.  They're not even in the same league as sources.   Sławomir Biały  (talk) 21:48, 30 November 2011 (UTC)
 * It's a much better tertiary source, but still, ideally we should not be citing tertiary sources. I do absolutely stand by my assertion that all citations to tertiary sources should be removed, not just added to, once adequate secondary sources are found.  As I say, external links are a different matter; for convenience's sake it's probably reasonable to put the links there. --Trovatore (talk) 19:03, 1 December 2011 (UTC)

Couple of comments here. First, Nbrothers (and everyone else) wants to fix the articles where the change of the template hs led to bad outbound links to EOM's new site. These links would have the new website, but the old id piece so something like http://www.encyclopediaofmath.org/index.php/f/f041470.htm any way that we can do an intelligent search for that? Secondly, I think that using interwiki would be great not directly used for reference which would have an oldid. Thirdly, references are held to a different level of reliability than interwikis. It is entirely possible for the decision to be one of three. Use for ref and 'see also's, use only for 'see also's and don't use at all.Naraht (talk) 11:36, 1 December 2011 (UTC)

I see really nothing wrong with citing tertiary sources, what matters first and foremost is whether they are reputable and reliable not whether they are secondary or tertiary. If you would argue strictly against reliable tertiary sources, you could even cite most math textbooks, which are tertiary sources as well. Moreover good tertiary sources may even offer another layer of error correction and can be more comprehensive than individual secondary sources. As far as "inferior" tertiary sources such as MathWorld are concerned, use them where they work and don't use them where they don't. There is plenty of basic stuff where you can use MathWorld without any problems and in doubt it is better to such topics in WP sourced with MathWorld than not having it sourced at all. In areas where MathWorld's descriptions become iffy or questionable just don't use it.--Kmhkmh (talk) 01:35, 11 December 2011 (UTC)

Hans Rådström
A mathematical reviewer is requested. Thanks for your interest. Kiefer .Wolfowitz 15:18, 17 December 2011 (UTC)


 * ... that Swedish mathematicians Lars Hörmander (pictured) and Hans Rådström isometrically embedded the nonempty, compact convex subsets of a vector space as a convex cone in a normed space?

Mikhail Kadets
Besides his work on HR, editor Sodin/Sasha wrote the following biography, which will interest functional analysts and probabilists:


 * ... that the mathematician Mikhail Kadets became interested in the theory of normed spaces after reading the Ukrainian edition of the French treatise by the Pole Stefan Banach?

Created by Sodin (talk). Self nom at 23:35, 16 December 2011 (UTC) Well done! Kiefer .Wolfowitz 15:18, 17 December 2011 (UTC)

wikibooks
I was editing the article on Euler's totient. In the section [] there are a number of summataion formulae without source. The only on-line source I could find was

Is this considered a reliable source? If so how should I reference it?

Thanks

Virginia-American (talk) 18:25, 17 December 2011 (UTC)
 * You could also try asking on WP:RS/N but my opinion is no, it falls under WP:USERGENERATED. —David Eppstein (talk) 18:29, 17 December 2011 (UTC)


 * Agreed. Wikimedia sites (Wikipedia, Wikibooks, etc.) are not reliable sources (except in rare cases like when Wikimedia is the subject of the article). CRGreathouse (t | c) 03:00, 19 December 2011 (UTC)

Articles for creation/Proof that the set of super-prime numbers is small.
Would someone in this project familiar with maths articles please determine the future of Wikipedia talk:Articles for creation/Proof that the set of super-prime numbers is small. and use the links on the AFC template to prompote this as an article or else provide feedback to the author. thanks --Tagishsimon (talk) 01:23, 19 December 2011 (UTC)

Articles on close subjects which are not interreferenced
I am afraid by the number of pages dealing with almost the same subject which are not of badly inter referenced. Recently, in this talk page we came on the various meanings of "normal" with no reference to curvature vector nor to binormal vector. Looking to curvature, I have remarked (and corrected) that radius of curvature and curvature were not inter referenced. Earlier in this page, we have encountered the same problem with algebraic number field and global field. I have recently corrected the same problem between dimension of an algebraic variety and Krull dimension. Is there a systematic way to solve this issue? May be a subproject of this project? D.Lazard (talk) 16:54, 19 December 2011 (UTC)


 * Algebraic number field and global field are inter-referenced as I understand that term (i.e. each has a link to the other). Do you mean something different? I do think that it would make sense to mention the generalization of algebraic number fields to global fields in the lede of Algebraic number field; perhaps this would work for other examples as well. RobHar (talk) 21:30, 19 December 2011 (UTC)


 * All examples I have given have been resolved recently by my edits. In the case of global function field, the problem was that there were no link, nor direct nor indirect from the disambiguation page function field to global function field. I have opened this discussion because a too large part of my edits is devoted to solve this kind of problems.


 * Another example of this is the ongoing discussion and ongoing vote in Talk:Vertical angles where the question is (for me) ''what to do with several pages which are essentially reduced to a definition, when this definition is given independently in angle? D.Lazard (talk) 11:34, 20 December 2011 (UTC)

Strict conditional
The article Strict conditional may need some attention. -- 202.124.75.203 (talk) 23:36, 19 December 2011 (UTC)


 * Strong Keep. Keep current (revised) version. I will point out that at this point I have addressed each and every concern the IP 202.124.75.203 (talk) has raised. The IP has not done the same for me. It is also clear the IP has failed to understand the cited sources. A merge was agreed upon in talk, and so I have gone ahead with the merger. The article is now full and complete. For more detail, see Talk:Strict conditional and WikiProject philosophy. Also note the contender is masked behind a random IP, unwilling to take responsiblity for its ungrounded claims. I, on the other hand, am a registered user of Wikipedia. As such, I am willing to take full responsibility for my edits, editions, and contributions to the site. I strongly recommend keeping the current (revised) version of this page. Hanlon1755 (talk) 16:07, 20 December 2011 (UTC)
 * For some context, it may be helpful to point out that User:Hanlon1755 has caused the whole recent kerfufffle by creating the new article Conditional statement (logic) (now redirected) and then nominating for deletion the existing one strict conditional. —David Eppstein (talk) 16:36, 20 December 2011 (UTC)

Matrix Chernoff bound
Re. Wikipedia talk:Articles for creation/Matrix Chernoff bound

Help, please.

Can some mathematician please check out Wikipedia talk:Articles for creation/Matrix Chernoff bound.

If it's acceptable as an article (ie, unlikely to be deleted), please just move it to a live article, and remove the header.

If not, you could explain why directly on that page, and leave a note for the author.

Thanks,  Chzz  ►  08:15, 20 December 2011 (UTC)


 * I've accepted the article, so it is Matrix Chernoff bound. If it's wrong, just fix/delete it. Thanks,  Chzz  ► 12:26, 20 December 2011 (UTC)

Sendov's conjecture
Sendov's conjecture is a new article. If you're so inclined: Michael Hardy (talk) 18:58, 18 December 2011 (UTC)
 * Improve the article; and
 * Add additional appropriate links to it from other articles.
 * Because of the opening sentence, I think its worth noting that at the moment Critical point (mathematics) refers only to functions of real variables, this needs to be extended. Brad7777 (talk) 17:01, 21 December 2011 (UTC)

Music Theory
At the moment Category:Music theory is found under the parent Category:Mathematics. Having a look at some of the articles of Category:Music theory because i have little knowledge of it, it seems that it is not purely mathematical, but should Category:Music theory be under Category:Mathematics of music instead or should only the specific articles relating to the mathemathematics of music be placed in it, with Category:Music theory being removed from Category:Mathematics? Brad7777 (talk) 16:45, 21 December 2011 (UTC)
 * And then there are articles like Hexany that have a music category and a math category but are not in any category that overlaps both hierarchies... probably also a flaw in our categorization. —David Eppstein (talk) 17:06, 21 December 2011 (UTC)
 * I think Category:Mathematics of music should be renamed.Category:Mathematics of music would be less exclusive if it was renamed to Category:Mathematics and music (or Category:Music and mathematics). The main article of this category is [[Music and mathematics, which is also in Category:Mathematics and culture. Category:Mathematics and music could be a subcategory of Category:Mathematics and culture.Category:Mathematics of music is at the moment a subcategory of Category:Music theory and Category:Applied mathematics, Im not sure how these would be affected. Brad7777 (talk) 17:52, 21 December 2011 (UTC)

Mainstream music theory is not part of mathematics (although some people would have us believe that there is a mathematical flavour to it). There is some valid mathematics to be done in the fields of intonation (part of music theory) and acoustics (generally not considered a branch of "music theory", rather some combination of science and engineering). And there are some small connections between mathematics and some ways of viewing musical structure, e.g. people finding the golden ratio in the works of some composers, and Ligeti drawing inspiration from fractals and chaos. Also some bad pseudoscience in alleged applications of things like group representation theory and axiomatic set theory to the theory of harmony (the article Transformational theory is at the respectable end of this; it gets much worse, but there's not much of this on Wikipedia so far).

My feeling is that Category:Mathematics of music should be a subcategory of Category:Mathematics as well as of Category:Applied mathematics (oddly, applied mathematics is not part of mathematics according to our category system!) but Category:Music theory should not have any mathematics categories as parents; there is plenty of scope for articles to belong to more than one category here. Jowa fan (talk) 03:21, 22 December 2011 (UTC)

Proper procedure for archiving talk pages
Hi, I was just noticing how long the talk page for l'Hopital's rule is (some of the comments are from 2003 and there are 40 subsections) and I was wondering how to go about archiving some of that. I'd like to see how that's done, if possible. Thanks! Rschwieb (talk) 01:01, 22 December 2011 (UTC)
 * See Help:Archiving a talk page and User:MiszaBot/Archive HowTo. JRSpriggs (talk) 02:59, 22 December 2011 (UTC)
 * Thank you :) Rschwieb (talk) 18:23, 22 December 2011 (UTC)

Articles on Swedish mathematicians
Hello colleagues,

a reviewer is needed for two mathematicians' DYK (one of them already mentioned above):


 * Hans Rådström (created by User:Kiefer.Wolfowitz), the nomination is here
 * Marcel Riesz (expanded by my humble self), the nomination is here

The article on Torsten Carleman has also recently been expanded (but is not nominated for DYK, so needs no effort from you)

Thank you very much for the help!
 * Sasha (talk) 21:36, 22 December 2011 (UTC)

I did the Riesz one. That's a lot more detailed and well sourced than most brand-new articles on mathematicians — well done. —David Eppstein (talk) 23:35, 22 December 2011 (UTC)
 * thank you very much! Sasha (talk) 02:14, 23 December 2011 (UTC)

Target for 'Normal line'
Currently Normal line, with a few other normal objects, redirects to Surface normal, which I found a bit surprising since I think of normals existing for objects with dimension other than 2. Perhaps expanding the scope of 'Surface normal' to include other normals with a corresponding change in name would be in order. Tangent covers some of this material as well but you'd have to know to look there.--RDBury (talk) 20:03, 18 December 2011 (UTC)
 * I'd say delete the redirect as having too much potential for ambiguity, given that it's unlikely to be helpful as either a search target or a link target.

--Trovatore (talk) 00:09, 19 December 2011 (UTC)


 * The problem is wider: the set of normal vectors is usually named normal vector space or "normal space", and it appears that a user searching for this is directed to normal space which describes a completely different notion and does not contains any disambiguation hatnote. D.Lazard (talk) 08:39, 19 December 2011 (UTC)
 * I have added a hatnote to normal space and a general definition of normal vectors in Surface normal. However it is yet needed of "expanding the scope of 'Surface normal' to include other normals with a corresponding change in name". D.Lazard (talk) 10:49, 19 December 2011 (UTC)
 * That's a definite improvement. I also support the idea of expanding the scope as described, though a suitable name escapes me, perhaps just Normal vector? It already has a generalizing section, but I think all dimensions should be given equal weight. At the moment the normal to a curve seems to be neglected (though a curve does qualify as a hypersurface in 2 dimensions). — Quondum tc 12:46, 19 December 2011 (UTC)
 * I think 'Normal vector' is still too specific. The sentence I'm trying to wikilink is "The radius of curvature is the length of the line normal to the curve between it and the x-axis." There isn't a vector or surface in sight. Since "the normal" can mean normal line, normal vector, etc. depending on the context, how about Normal (geometry)? Subtangent already covers some archaic phrases such a "polar subnormal".--RDBury (talk) 13:37, 19 December 2011 (UTC)
 * Normal (geometry) is a good name. However I do not imagine in which context the sentence "The radius of curvature is the length of the line normal to the curve between it and the x-axis." may be mathematically correct, as the radius of curvature is an invariant which does not depend on the choice of the x-axis. D.Lazard (talk) 14:26, 19 December 2011 (UTC)
 * I concur with as a name. Perhaps swap Normal (geometry) and Surface normal, with the latter redirected to the former? Editing the content would follow more naturally once that's done. — Quondum tc 15:29, 19 December 2011 (UTC)
 * (Update) I went ahead and made the move, the article now needs some cleanup and links need to be updated. To D.Lazard, the statement is true for a specific curve (the catenary) and a specific choice of x-axis. It is equivalent to the differential equation y′′y=y′y′+1.--RDBury (talk) 16:15, 23 December 2011 (UTC)

General proof of l'Hopital's Rule needs your vetting
I have tried to reason with Rschwieb about this, but he decided to ignore my concerns, regardless of the fact that it is purely logic and math based, pointing out errors in his current proof in the article. I'm looking for a mediator in this, someone who can address the mathematical issues I bring forth in Talk:l'Hôpital's rule. Thanks. Toolnut (talk) 11:17, 22 December 2011 (UTC)
 * My feeling is that the general proof shouldn't be there at all. According to Manual_of_Style/Mathematics, the reason for including a proof is to illustrate a concept.  The proof of the special case is enough to achieve this; there's no need for further detail. Jowa fan (talk) 11:58, 22 December 2011 (UTC)
 * I would agree with Jowa 100% when the proof is not the title topic. Recommendations for keeping or deleting are welcome.
 * Context: There was a pretty messy and incomplete proof in that article. Toolnut proposed his own OR proof, but Duoduoduo and I dissuaded him and counterproposed the adaptation of a published proof by A.E. Taylor. In one line Taylor's notation is not perfectly clear (Toolnut calls it "Taylor's error"), and I strove to give the most obvious interpretation. Nothing Toolnut raised cast doubt on the interpretation. Naturally he doesn't think so, and he made it clear he wasn't going to consider anything but his version, I gave up on listening.
 * If we do not keep the current version, I recommend either Taylor's exact notation be reinstated, or that the whole proof section be removed. Rschwieb (talk) 18:22, 22 December 2011 (UTC)
 * We don't normally include proofs unless they are noted as interesting or notable somewhere, not just that they have appeared in a textbook or else are short enough not to be a bother. If there's some interesting step in it then an outline is a good idea otherwise that's what citations are for.
 * I have myself removed some maths that was cited correctly to a book because it was simply wrong but in general actions like that require a strong consensus that there is something definitely wrong. We start with the assumption the books are right and trump people's personal opinions. Dmcq (talk) 23:56, 22 December 2011 (UTC)
 * I agree.  Sławomir Biały  (talk) 00:43, 23 December 2011 (UTC)
 * Since the proof doesn't really have an outline version, I'll take these as recommendations for deleting the section. It would be nice to get a few more "do not includes" to make the decision to remove clear. Or if nothing is said in a week, I'll take it out. Rschwieb (talk) 12:42, 23 December 2011 (UTC)

list of sums?
In our Lists of integrals we can learn that
 * $$ \int_0^\infty \frac{x}{e^x-1}\,dx =\frac{\pi^2}{6}, $$

and all sorts of other things like that. Do we also have a list of sums? If not, we probably should. Michael Hardy (talk) 19:44, 22 December 2011 (UTC)


 * I think List of mathematical series covers what you have in mind, though it could have a more accessible name perhaps.--RDBury (talk) 16:23, 23 December 2011 (UTC)

Please help fix mathematics disambiguation links
Please help - we need your expertise to fix the large number of disambiguation links to Positive definiteness: 59 links; Lemniscate: 39 links; Plane geometry: 38 links; and Random number: 37 links. Alternately, please consider whether all of these pages should be disambiguation pages. Perhaps, for example, an article can be written encompassing the various concepts of a "random number" or a "lemniscate" curve. Cheers! bd2412 T 19:28, 9 December 2011 (UTC)


 * Fixed for plane geometry by renaming it as plane geometry (disambiguation) and redirecting plane geometry to Euclidean geometry. D.Lazard (talk) 23:14, 9 December 2011 (UTC)
 * Thanks, I appreciate this solution! bd2412  T 17:07, 10 December 2011 (UTC)
 * "Lemniscate" is a generic term for any figure eight curve, so unless the article is referring to a specific one there is no way to resolve the link. I doubt there would be enough material to make an article on the generic term, and the notable lemniscates are too different mathematically for a merge to make sense. Perhaps if the word is used in a generic sense the best solution is to replace it with "figure eight curve" which shouldn't need a link at all.--RDBury (talk) 15:36, 10 December 2011 (UTC)


 * I thought I was doing something ridiculous as I changed lemniscate to lemniscate of Bernoulli in Deep Secret. Perhaps it would be reasonable to keep the links to lemniscate, and add a sentence there that it is also a generic term for the figure-eight curve. Sasha (talk) 15:57, 10 December 2011 (UTC)


 * I do not agree that "the notable lemniscates are too different mathematically for a merge to make sense". The notable lemniscates are exactly the quartic curves of genus 0, symmetric with respect to the axes, with a crossing point at the origin and the other singular points at infinity, which are either cyclic or contact of two tangent imaginary branches. Thus they fit in a single definition. I am preparing a introduction for the page lemniscate, for saying that in an elementary way, before linking to the existing pages. Once this will be done, it will be easier to discuss if a merge make sense of not. D.Lazard (talk) 16:50, 10 December 2011 (UTC)
 * Please note, I do not propose a merge of any articles, merely the creation of a broad concept article with discussion of each of the concepts identifiable as falling under it, with links out to these individual concepts. In particular, I doubt that random number needs to be disambiguated, because it seems that the articles listed there are merely means by which a number can be random, or by which a random number can be generated. bd2412  T 17:18, 10 December 2011 (UTC)


 * The Lemniscate of Bernoulli is actually a special case of the Lemniscate of Booth but in terms of how they are defined they are very different. They are bicircular while the Lemniscate of Gerono is not, and that is defined differently as well being a lissajous figure. Actually the Lemniscate of Booth is in turn a type of hippopede which is where the link takes you. The Conditions you give may define a family that includes all these curves, but it's not the definition of lemniscate that I've familiar with. Though if you can find a reliable source for it then go ahead and put it in the article. I added a link to Watt's curve to the page since it is, to my mind at least, a Lemniscate, though it doesn't fit your definition.


 * Anyway, I've fixed about twenty of the links so far, some by replacing the term with "figure eight", some by finding a better target for the link, some just one-offs because the situation is unique. Much of the time figure eight works just as well and the person who added the term apparently just wanted to be abstruse. You have to wonder what was going though the mind of the editor who thought that someone reading the article on the children's book Little Toot and wanted more info on a figure eight would want to be linked to an article on algebraic geometry.--RDBury (talk) 17:23, 10 December 2011 (UTC)


 * I think lemniscate is done now, the only two articles left (not counting redirects and other dab pages are List of geometric shapes and Figure 8 where it's probably just as well to leave them. I also fixed links to Lemniscus since it was easy.--RDBury (talk) 18:17, 10 December 2011 (UTC)

Another mathematics disambiguation page with a large number of incoming links is Linear least squares: 37 links. Cheers! bd2412 T 17:39, 10 December 2011 (UTC)

Here's one more - Generating set: 39 links. It might be helpful if someone from this project were to peruse Disambiguation pages with links/December 2011 to see if there are other pages with solutions for which mathematical expertise would be useful. Cheers! bd2412 T 02:49, 11 December 2011 (UTC)


 * Here are some more math-related dab pages. I can't guarantee that all of these have math content, but they all have the possibility:
 * Some uses of functional
 * Some uses of interval
 * Function field— ✅. All links from article namespace have been disambiguated. — D.Lazard (talk) 16:40, 26 December 2011 (UTC)
 * There is a problem here: Most links intend to link to the function field of an algebraic variety. The others intend to link to a second meaning: A function field may be an algebraic extension of the field of the rational functions over a field (usually a finite field of the field of the rationals). The importance of function fields lies in the fact that they are strong analogues of the number fields, in the sense that almost every result on number fields has an equivalent for function fields, frequently easier to proof. The article Number theory in function fields seems lacking. How to solve properly this issue? D.Lazard (talk) 11:51, 14 December 2011 (UTC)
 * For beginning to solve this issue, I have created the redirect function field (algebraic geometry) and added 3 links in function field, including a red link to function field (number theory). D.Lazard (talk) 12:21, 14 December 2011 (UTC)
 * I have fixed the issue by using a useless redirect for creating a page algebraic function field which is a better name than function field (number theory). I have also updated the dab page. Thus it should become easy to fix the links to this disambiguation page by choosing, in each case, between function field of an algebraic variety and algebraic function field. D.Lazard (talk) 14:04, 14 December 2011 (UTC)


 * The function fields that are analogues to number fields are the global function fields, which already appear in the article Global field, so there is no need for function field (number theory) right now. If the material were to expand, it would make sense to make an article called "global function field" (maybe with a redirect from "function field (number theory)"). But algebraic function field is not a replacement for "global function field". In fact, the algebraic function fields you've defined are simply the function field of an algebraic variety, so the article is redundant. Moreover, the latter article has some issues: "More precisely, in complex algebraic geometry the objects of study are complex analytic varieties". Umm, no, that's complex analytic geometry. Accordingly, the article has some poor ratings. And that mistake has been in there since 2006! I think algebraic function field and function field of an algebraic variety should be merged. RobHar (talk) 16:07, 14 December 2011 (UTC)


 * I have missed global field. I have added a link to it in algebraic function field. Algebraic function field is not redundant with function field of an algebraic variety because "algebraic function field" is a well established terminology in mathematical fields which are not subfields of algebraic geometry (to be convinced, ask "algebraic function field" to Google scholar). Thus Wikipedia users may be interested in algebraic function fields without knowing anything about algebraic varieties. If one consider the present state of global field and algebraic function field, they could be merged, but I believe that it is not a good idea, as both articles are stubs which deserve to be expanded in completely different directions. D.Lazard (talk) 10:34, 15 December 2011 (UTC)


 * I just think that having two separate articles on algebraic function field and function field of an algebraic variety creates a content fork. Either merge one into the other (and leave a redirect) or merge them both into a new article with a new title. The point is that they are the same thing. RobHar (talk) 22:11, 15 December 2011 (UTC)


 * Some uses of stack
 * Variable
 * Possibly some rare instances of cleavage -- I don't think there are any math-related ones here. --Joel B. Lewis (talk) 22:23, 15 December 2011 (UTC)
 * Some uses of digraph -- ✅. The only article pages leading to digraph are the redirects digraphs and diagraph.  It seems like digraph (orthography) is by far the dominant usage, so perhaps digraph should direct there (rather than to the disambiguation page) by default. --Joel B. Lewis (talk) 19:05, 15 December 2011 (UTC)
 * Isometric
 * Some uses of commute — ✅. All links from article namespace have been disambiguated. —David Eppstein (talk) 22:38, 13 December 2011 (UTC)
 * Thanks, I have noted this on the disambig project page. Cheers! bd2412  T 16:35, 14 December 2011 (UTC)
 * Fixed-point theorem
 * Hypergeometric series
 * Lie bracket
 * Some uses of localization
 * Some uses of segment
 * Ozob (talk) 03:34, 11 December 2011 (UTC)
 * Thanks! Any help getting through these (or determining if they need not be disambiguated) is very much appreciated! bd2412  T 22:34, 13 December 2011 (UTC)

Request check of change to Monodromy
Can someone please look at the following change to Monodromy ( http://en.wikipedia.org/w/index.php?title=Monodromy&action=historysubmit&diff=467516318&oldid=465625556), I'm not sure if it should be removed or just altered...


 * It's a little out of place, but I don't think it particularly hurts anything. I say leave it in.  Change it as you see fit, though.   Sławomir Biały  (talk) 22:36, 25 December 2011 (UTC)

Ars inveniendi
is ars inveniendi a true notion or jibberish? I do not understand a single word there.

Sasha (talk) 05:18, 27 December 2011 (UTC)


 * Just a piece of philosophy, see Mathesis universalis; why bother? Boris Tsirelson (talk) 05:48, 27 December 2011 (UTC)


 * I have not heard these Latin phrases before. However, just as one may suppose that biology is reducible to chemistry and that chemistry is reducible to physics, so one might suppose that physics is reducible to mathematics. All that is required is some way of mapping our subjective experiences into a mathematical model (of the physical world). JRSpriggs (talk) 07:25, 27 December 2011 (UTC)


 * thanks! I do not bother, I just saw it on the list of new articles and wondered. Sasha (talk) 13:59, 27 December 2011 (UTC)

Math stub templates
There's a discussion about possibly renaming a bunch of math stub templates at Stub_types_for_deletion/Log/2011/December/28. The full list is at Category:Mathematics stubs. This might be a good time to consider whether renaming them is worthwhile. The discussion should probably happen at the "Stub types for deletion" page, which is not accurately named. &mdash; Carl (CBM · talk) 14:16, 28 December 2011 (UTC)

Ellis–Numakura lemma
I think that Ellis–Nakamura lemma should be moved to Ellis–Numakura lemma. I've brought it up here for two reasons. 1. Perhaps someone more familiar with this area of mathematics could check this. 2. I am not familiar with the procedure for moving pages. --Kompik (talk) 17:07, 28 December 2011 (UTC)


 * The name was definitely misspelled. David Eppstein has moved the article to the right title. I'm glad you noticed this. &mdash; Carl (CBM · talk) 17:20, 28 December 2011 (UTC)


 * I guess the reason was that it appeared in this spelling in Terrence Tao's blog post. Thanks a lot for your help! --Kompik (talk) 17:23, 28 December 2011 (UTC)

Mathematical comparisons
Why do we have Category:Mathematical comparisons? Brad7777 (talk) 12:45, 26 December 2011 (UTC)
 * no reason known to me. Nominate for deletion? Sasha (talk) 20:24, 26 December 2011 (UTC)
 * I think so Brad7777 (talk) 20:15, 29 December 2011 (UTC)
 * Please keep Category:Comparisons of mathematical software, though. Leonxlin (talk) 04:32, 30 December 2011 (UTC)

How to reference proofs and derivations
There is a thread at Wikipedia talk:Manual of Style/Mathematics on the preferred way to reference proofs and derivations. Neither the Scientific citation guidelines or WikiProject Mathematics/Proofs is very specific about this other than saying that they should be referenced.--RDBury (talk) 19:36, 29 December 2011 (UTC)

Help needed for the new version of algebraic geometry
The following text is copied from Talk:Algebraic geometry. However there are few intervention in this talk page. Moreover, I think that the main page of an area of mathematics is of interest for the whole wikiproject. Therefore I post it here also.

I have just rewritten a large part of algebraic geometry. One of the aims of my edits was to better covering the various sub areas of modern algebraic geometry: except for the scheme theory and its generalizations, none of them were even mentioned in the previous version. My guideline for my edits was Did you know that algebraic geometry is not as esoteric as it could seem?

Reviews and comments would be of great help to improve the result.

I need also some specific help to finish the work. Here is a list of the main points on which I need more specific help:
 * List of subareas: I have omitted to mention algebraic group theory and certainly other subfields. Thus the list of subareas in the lead has to be completed.
 * Each sub area of algebraic geometry deserve a section, especially, the relations between algebraic geometry and number theory, but probably also algebraic group theory and singularity theory. I have not the competence for writing them.
 * Section Modern viewpoint renamed Abstract modern viewpoint: this esoteric section is of no help for everybody. In fact most readers, even those like me which have some knowledge of algebraic geometry, have never heard the name of most theories which are cited, and can understand nothing in this section. The few other ones know the subject and do not get new information. Thus this section has to be rewritten for explaining why these theories have been introduced, which problems of general interest they have solved and why it may be interesting to learn them. If this may not been explained, these theories have not their place here but in a new article Extensions of scheme theory. I am not competent enough to rewrite this section in this spirit and thus need help for that.
 * Section Applications is a biased stub: Clearly a stub. Biased because it does not mention the applications of algebraic groups in theoretical physics nor the use of algebraic geometry in public-key cryptography and in algebraic cryptanalysis. I have not a clear view of what has to be done. A possibility is simply to suppress this section and replace it by sections Algebraic geometry and cryptography and ''Algebraic geometry and theoretical physics. This has to be discussed.

Good new year 2012 D.Lazard (talk) 12:40, 29 December 2011 (UTC)
 * Mon chapeau. That's a vast subject!  A more modest goal would be to improve the template Template:Algebraic_curves_navbox and the pages mentioned therein.  Tkuvho (talk) 13:19, 29 December 2011 (UTC)
 * Thanks for the comments. I do not think that improve ... the pages mentioned therein is a modest goal. In fact, I have edited algebraic geometry, because, after reading and editing many pages related to algebraic geometry, I came to the conclusion that wikipedia is very poor on the part of the algebraic geometry which is outside scheme theory and is not limited to dimension 2 and 3. For example, before my edits, the page dimension did not mention the dimension of an algebraic variety and the page dimension of an algebraic variety presented the only definition (among at least 10) which may not be extended to algebraic sets. Therefore, my primary goal, when rewriting algebraic geometry was to have a correct starting point to navigate inside algebraic geometry. D.Lazard (talk) 15:11, 29 December 2011 (UTC)
 * Thanks for the clarification. So your goal was precisely to get away from low dimensions, at variance with my proposal... Certainly improving the coverage on algebraic sets is a worthwhile goal.  Tkuvho (talk) 16:10, 29 December 2011 (UTC)
 * I am curious to know what you think could be improved with the navbox. The layout?  The choice of topics?  I was never convinced that I had gotten it right, but I didn't know how to make it better.  Ozob (talk) 22:58, 29 December 2011 (UTC)
 * The template looks great to me. I was only making a general comment (not implying a criticism of the template).  In fact, the template should be added to all the pages listed on it.  Some of the pages could use further work. Tkuvho (talk) 10:19, 30 December 2011 (UTC)

The treatment of scheme theory in the main algebraic geometry article is a bit heavy-handed. I don't see why every conceivable topology and every generalization of schemes should be mentioned, particularly not when the basic idea of a scheme as an object that is "locally like an affine variety" is completely absent. I'm not sure how this content should more appropriately be reconfigured, but I do support a substantial overhaul of the article, and I think Lazard's suggestions are very worthwhile. I don't think, though, that we should spurn dimensions 1 and 2 since these are the greatest success story of algebraic geometry. Rather, I think we should have a section on curves and a section on surfaces, in addition to the kinds of things Lazard suggests. Sławomir Biały (talk) 23:09, 29 December 2011 (UTC)

I just want to say a great work: it is important to have well-balanced articles on general subjects. But the absence is equally problematic as precence (cf. the above). Thus, the following should be covered (but not limited to): defomation theory, intersection theory, geometry of positve characteristic (i.e., Mumford), arithmetic algebraic geometry, geometric invariant theory, resolution of singularities, toric varieties, algebraic groups (e.g., linear algebraic groups, abelian varieties, Jacobian varieties), more generally representation-theoretic stuff), cohomological stuff (e.g., Serre duality, standard conjecture), algebraic vector bundles, smooth morphisms (we "really" need an article on it), elliptic curves, classical classifications (e.g., Italian classification of surfaces, Kodaira classifications), Mori program, algebraic stack, theory of descent (connection to Galois descent), Neron models, conspiracy theory (algebraic geometers taking over the rest of mathematics.)

I agree that the scheme-theoretic matters should be minimized: scheme-theretic fibers v.s. set-thereotic ones, functor of points point of view. A better appraoch is to constrast different approaches: scheme-theoreitc ones, Weil-type stuff (i.e., field of definition) and complex-analytic approach (i.e., Griffiths-Harris). I'm not so sure how much commutative algebra stuff should be there: multiplicities, Hilbert polynomials, Nakayama lemma in geometric language, etc. -- Taku (talk) 15:01, 30 December 2011 (UTC)


 * These also seem mostly like sensible suggestions. I think a primary consideration at the moment is to grow the article (as well as nearby articles) to include a more comprehensive treatment of the subject.  Ultimately, we might need to reconfigure content across other articles as the main article grows.   Sławomir Biały  (talk) 15:13, 30 December 2011 (UTC)

Typography for "Big oh" notation
Hi all. On several pages where big-oh notation is used and not rendered in TeX, the result looks like an enormous alpha on my screen. I didn't recognize it at all, at first. Am I at cross purposes with any existing policy if I append \, to these expressions to force them to render differently? Thanks, Rschwieb (talk) 19:24, 29 December 2011 (UTC)


 * It would probably be better to fix the underlying problem, since I don't think it's practical to find every use of big-O notation on Wikipedia. Can you give an example of a page and an equation that looks bad for you?  Ozob (talk) 22:54, 29 December 2011 (UTC)


 * It first caught me off guard at Euler_trail. At standard magnification in my Internet Explorer 9, $$O($$ looks like a single character. I'm sure I could swtich up browsers somehow, but I don't really care for my own viewing experience as much as I care that it might be a stumbling block for other unsuspecting readers. The article Big O Notation is almost completely free of that rendering, except for one or two paragraphs. Rschwieb (talk) 13:57, 30 December 2011 (UTC)


 * I see, this is not a Wikipedia-wide issue but rather a browser-specific rendering issue. Usually I think that   translated into HTML renders okay, but in this case it's pretty bad.  That same paragraph contains $$O(|E|\log^3|E|\log\log|E|)$$, which on Safari 5.1.2 and Firefox 8.0.1 looks pretty awful (there are big gaps around the |'s).


 * I still don't think it's realistic to convert every use of O into either PNG or pure HTML, but I wouldn't object if someone did that to the worst-looking instances. In the long term, our TeX rendering will hopefully be better... Ozob (talk) 19:52, 30 December 2011 (UTC)


 * Yeah, it was never my intention to uniformize the notation, I was mainly looking for license to make the change where it seemed most ugly. I'll take this as an "OK". Thanks for your input, Ozob. Rschwieb (talk) 22:33, 30 December 2011 (UTC)

There are several discussions on this in Talk:Big O notation, most recently Talk:Big O notation. I'm not sure the consensus is clear but the majority opinion seems to be that we should be using a simple italic capital O rather than a fancy calligraphic capital O. —David Eppstein (talk) 21:31, 30 December 2011 (UTC)

Some irrational constants and Template:Irrational numbers
Take a look at Template:Irrational numbers. The articles ζ(3), √2, √3, √5, ρ, δS all feature the template on inside a funny table (frankly, not too attractive) showing the numbers in different bases. Tables showing similar information on &gamma;, φ, and π look slightly better. (α, δ, and $e$, do not seem to have the table.) While all these tables have the same type of content, they are apparently not templates, but one-time formatted tables in each instance.

Is there a reason why there isn't a special infobox set up for constants like these? It would be a good idea on these pages to standardize via template the formatting of a few pieces of information, such as the decimal expansion to 20 or 50 places and whether the number is irrational or transcendental, I think. Currently, different numbers of places are shown for the golden ratio, e, and π.

I also notice that there's a Template:Infobox number, but it doesn't seem particularly well-suited to non-integers. (Furthermore, the integers -1 through 9 don't seem to use the template for some reason.) Leonxlin (talk) 05:14, 30 December 2011 (UTC)


 * 'Infobox number' is designed for articles on integers and there a few non-optional parts that would not be appropriate for non-integers. Imo both the templates get a bit silly in the type of information they provide. for example do we really need the binary expansion of the Plastic number or 9814072356 in Roman numerals? The 'Irrational numbers' template shouldn't be used more than a dozen times, there simply aren't that many non-integers that meet notability criteria, so I don't see the need to make it more elaborate than it already is. It should be easy enough to make the articles consistent manually, though I'm not convinced the need for this is very urgent.--RDBury (talk) 14:55, 30 December 2011 (UTC)
 * How about just getting rid of 9814072356 entirely.Naraht (talk) 22:39, 30 December 2011 (UTC)

Andrey Markov Jr.
I have proposed to move Andrey Markov (Soviet mathematician) to Andrey MArkov, Jr. See here. Sasha (talk) 17:33, 31 December 2011 (UTC)
 * Done. Tkuvho (talk) 21:02, 31 December 2011 (UTC)